(1) Field of the Invention
The invention is generally related to the field of signal processing, and more specifically to the determination of the onset of turbulence in connection with a body moving through a fluid medium.
(2) Description of the Prior Art
The boundary layer flow over a body which has an axisymmetric exterior surface moving through a stationary fluid, in which the motion is steady and directed parallel to the longitudinal axis of the body, may be characterized by three spatially separated, but somewhat over-lapping, flow zones. These zones may be described as a laminar zone, a transitional zone and a turbulent zone. In the laminar zone, which is generally located toward the leading edge of the body, there are no appreciable disturbances of the pressure of the fluid on the surface of the body, and hence any measured pressure fluctuations within this zone are appreciably negligible. As the flow develops downstream of the leading edge of the body, it enters into the transition zone. The transition zone evolves from the latter stages of the laminar flow, where infinitesimal, linear wavelike disturbances, so-called Tollmien-Schlichting (T-S) waves, develop and begin to amplify both temporally and spatially with distance downstream of the leading edge of the body. The position along the wall at which small disturbance waves begin to amplify is related to both the shape and size of the body, as well as inertial characteristics of the flow of the medium in the vicinity of the wall. A re9ion of decreasing velocity (or increasing pressure) of the fluid relative to the surface of the body downstream of the leading edge of the body marks the beginning of a zone where an adverse pressure gradient sets in. This adverse pressure gradient has a destabilizing effect. At or shortly downstream of this position, T-S disturbance waves would be expected to start to grow.
The amplitude of the T-S waves becomes larger as they convect downstream, and as a result their evolution becomes nonlinear and turbulent bursting is observed. The bursts initially are local and occur intermittently over each point over this portion of the surface of the body. The number of bursts per unit time increases with distance along the surface from the leading edge of the body. Downstream, the bursting finally coalesces in such a way that the flow reaches a fully turbulent state. The position along the wall where bursting fully coalesces is the dividing line between the end of the transitional zone and the start of the turbulent zone.
Nonlinear coupling of energetic modes in the spectra of fluctuations in the velocity of the medium proximate the sidewall of the body, or of fluctuations in the pressure exerted by the medium on the sidewall of the body following T-S wave amplification. The nonlinear nature of the transition produces a temporal power spectrum of frequencies of the T-S waves and combinations of the sums and differences of the respective frequencies. In the time domain, the time scales of interest are the reciprocals of the associated T-S frequencies. These principal time scales are characterized by a value corresponding to the wavelengths of the T-S waves divided by their convective velocities.